Simulator



R. G. PIETY March 23, 1954 SIMULATOR 4 Sheets-Sheet 1 Filed Jan. 2, 1955INVENTOR.

BY Ram Hua z P ATTORNEYS R. G. PIETY SIMULATOR March 23, 1954 4Sheets-Sheet 2 Filed Jan. 2, 1953 INVENTOR. flfiih'eiy WQW R. G. PIETYMarch 23, 1954 SIMULATOR 4 Sheets-Sheet 3 Filed Jan. 2, 1953 ATTOR/VEVJlu i U March 23, 1954 R6, PIETY 2,673,031

'SIMULATOR Filed Jan. 2, 1953 4 Sheets-Sheet 4 OSCILLATOR AMPL/F/L-A A l:1 x

AMPL/Hfk A/VD DEMON/1.117101? INVENTOR! B. dip/Ly BY Patented Mar. 23,1954 SIMULATOR Raymond G. Piety, Bartlesville, kla., assignor toPhillips Petroleum Company, a corporation of Delaware ApplicationJanuary 2, 1953, Serial No. 329,280

14 Claims. 1

This invention relates to a simulator which is a mechanical analogue ofa pumping system. In one specific aspect it relates to a simulator whichis a mechanical analogue of the tubing, sucker rod, oil column, and pumpin a deep well pumping unit.

A typical deep well pumping system includes a series or string of metalrods, referred to in the art as sucker rods, which extend through tubingpositioned in the well, the lower end of which carries a pumping unit.The tubing, in turn, is suspended within a well casing end, under someconditions, the lower portion of the interspace between the tubing andeasing may contain a column of oil. At the top of the well, the suckerrod string extends through a stuffing box and is driven by a primemover, such as an electric motor or an internal combustion engine,throughv a flywheel or bull wheel. The flywheel, in turn, drives a crankor counterbalance which is coupled through a walking beam to the top endof the sucker rod string. c

As the pumping operation is carried out, a column of oil rises in theregion between the tubing and the sucker rod string, thus producing aviscous drag upon both the tubing and sucker rod. string. The weight andelasticity of the sucker rod string, as well as the tubing and oilcolumn, produce elastic strains in the pumping unit so that the suckerrod string and tubing behave in a manner somewhat analogous to elongatedsprings.

This elastic movement of the sucker rod strin and tubing oftentimesresults in failure of one or more sucker rods and, more often, ininefiicient operation of the pumping system. It has not been possible,in the past, to predict the effect of changes in various operatingvariables of the system with any degree of accuracy, except by purelyempirical or cut and try methods, for the obvious reason that themovement of the sucker rod string several miles below the surface of theearth cannot be observed nor is it possible to observe the manner ofoperation of the downhole pump.

It has been proposed to construct a mechanical model of the pumpingsystem so that adjustments of various operating variables of the scalemodel would produce effects thereon similar to the effects ofchangesincorresponding variables upon the actual pumping system.Unfortunately, to obtain any useful results by such a system, it can bedemonstrated mathematically that the scale model itself would be of suchlarge size and prohibitive cost as to render construction there'- ofentirely impractical. However, it has been discovered in accordance withthe present invention that a mechanical analogue of a pumping system canbe established on a practical scale. In this analogue system a series ofbars are connected in spaced relation between three pair of linesrepresenting, respectively, the oil column, the tubing, and the suckerrod string. The individual pairs of lines are coupled by damping memberswhich represent the viscous drag of the oil column on both the tubingand sucker rod string. The torques tending to rotate the various barsfrom their normal positions represent stresses imposed uponcorresponding elements of the sucker rod string, tubing and oil column,while the angular velocities and rotations of the bars represent thevelocities and displacements of corresponding parts of the pumping unit.In corresponding fashion, other parameters of the analogue or mechanicalsys- 1 tern represent corresponding variables and consystem may beutilized to predict the effect of changing various operating conditionsof the pumping system.

It is a further object to provide apparatus of the type described whichis simple to construct, reliable in operation, and which employs aminimum number of inexpensive components.

Various other objects, advantages and features of the invention willbecome apparent from the following detailed description taken inconjunction with the accompanying drawings, in which: Figure l is avertical sectional view, partially in elevation, of a typical deep wellpumping system;

Figure 2 is a schematic view of the analogue system simulating theoperation of the deep well couple viscously the various lines of theanalogue system;

Figure 8 illustrates apparatus simulating the downhole pump; and

Figure 9 is a schematic representation of the analogue surface pumpingunit and indicating system.

Referring now to Figure 1, there is illustrated, in a schematic manner,a typical deep well pumping system to which the simulator of thisinvention is applicable, this system including a driving mechanism itlocated at the surface and a downhole pumping unit ll. Unit ll includesthe usual well casing [2 within which is mounted a tubing l3 having asucker rod string [4 suspended therein, the latter including a number ofsucker rods it connected together by joints It. The upper end of stringl4 extends through a stufiing box 17 in a casing head it and the lowerend is attached to a plunger 19 forming a part of a pump iii whichincludes an upper or traveling valve 2i and a bottom or stationary valve22. The uppermost sucker rod or polished rod is driven by mechanism H)which includes a walking beam 24 secured at one end to the polished rodand at its other end is secured to a pitman 25 which is driven by acrank or counter-balance 2'6. Crank 26 is driven by a flywheel 21, asthrough a chain drive 28; and flywheel El, in turn, is driven by a primemover 29, as by a second chain. drive 351'. Prime mover 29 may be anelectric motor, an internal combustion engine, or any other suitabletype of engine.

In accordance with this invention, the operation of the downhole unit His mechanically simulated by the apparatus of Figure 2. The displacementtorques on various members of the analogue system represent stresses oncorresponding parts of the pumping unit, the rotations of variousmembers of the analogue system represent displacements of correspondingparts of the actual pumping system, and angular velocities in theanalogue system represent the velocities of corresponding parts of themechanical system. In order for the two systems to be analogues of oneanother, it is necessary that the equations describing the behavior ofthe analogue system be similar to the equations describing the behaviorof the actual pumping unit. Thereupon, by suitably adjusting thecoefficients of various terms of the analogue system, as by changing theparameters of various parts of the analogue system, a condition isobtained whereby the displacement torques, rotations, angular velocitiesand other parameters of the. analogue system correspond to the stresses,displacements, velocities and other related variables of the pumpingunit. At this time, the two systems are analogues of one another andfurther changes in the parameters of the analogue system produce effectsthereon which enable accurate prediction of the effects of correspondingchanges in the pumping unit.

In the simulator of Figure 2, a first pair of lines T and T representsthe tubing [3, a second pair of lines and 0' represents the oil column,and a third pair of lines R and R represents the sucker rod string l5.These letters are employed throughout the following description assubscripts to represent the line to which they are applicable, such asthe tubing, oil or rod line. The following notation is used in theequations to 4 be derived which define systems:

the motion of the two Pumping System Analogue System Zlength ofsucker-rod, oil column or tubing segment.

x", 1/, z,.displacement of sucker rod, oil column, and tubing siglnent,respectively.

an, 'uo, u weight per unit length of sucker rod, oil column and tubingsegments, respectively.

rod, oil column ant tubing segments, respectively.

an, I)", c,. acceleration o1 suclzcr rod, oil column, and tubingsegments, respectively.

p,., ,.-stress in sucker rod and tubingsegments,respectively.

q,.comprcssion in oil column segment.

e en, elelustic.modulus of the sucker rod, oil column, and tubing,respectively.

8,, s0 8zCl0SS sectional area of sucker rod, oil column, andtubingsogmcnts,respectively.

g-gravity constant.

lc,-viscosity constant relating to movement between sucker rod and oilcolumn segments.

Jar-viscosity constant relating to moveinentbctween Oll column andtubing segments.

11, o ;i,.-vclocit v of sucker d-length o1 sucker rod, oil

column, or tubing bars.

6,, 41,-, rl/,-rotation of sucker rod, oil column, and tubing bars,respectively.

,-, A,-, C,---moment of inertia of sucker rod, oil column and tubingbars, respcc tivel U,-, V,-, D,'-angular velocity of sucker rod, oilcolumn, and tubing bars, respectivoly.

04,-, 6;, 5,-cngu1ar acceleration of sucker rod, oil column, and tubingbars, respectively.

W. L, .Msuci:er rod, oil column and tubing bars, rcspcctivcly.

Krviscosity constant relating to movement between sucker rod and. oilcolumn bars.

K.,-visc0sity constant relating to movement between oil column andtubing barsv v r l i 4 i 1 le -viscosity constant relating to movementbetween tubing segments and fluids outside the tubing.

In the mathematical analysis of the pumping unit and analogue system.which follows, the respective equations are derived by the method offinite differences. In accordance with this method the casing, tubing,and sucker rod string are divided into a large number n of segments.During operation of the pumping unit each segment or" the sucker rod,tubing, and oil column moves upward or downward in accordance with themechanical laws governing the system. It has been discovered thatcorresponding equations describe the motion of the rotating lineanalogue system.

In particular, considering the nth segment 3 of the sucker rod, asdefined by the dotted lines 32 and 33, Figure 3, let it be assumed thatat a given instant the lower end of this nth segment is displaceddownward from its equilibrium position a distance can and the upper endof the segment is displaced downward from its equilibrium position adistance 1211-1. This displaced position is represented by 3 1. Such adisplacement results in a stretching of the nth segment by an amount$n$nl, which in turn results in a strain so that the total stress in thenth segment becomes:

Pn= T T( fl 7r-l2 In like manner a corresponding equation can be writtenfor the (n+1) th segment as follows:

"an upward viscous drag onthenth rod segment of magnitude krZWn-l-tu).From these datathe motion of a rod segment 34 which straddles the line33 can be deduced, this segment extending a distance The basic suckerrod equation is realized by combining Equations 1, 2, and 3 to obtain:

1' f T f (w .+1- 2zn+x.. 1)=- +k.z u,+v, -w,z

Equation 4 has its counterpart in the analogue system of Figure 2. Thisanalogue system comprises three pair of lines R, R; T, T; and. O,representing, respectively, sucker rod string l4,

tubing 13, and the oil column between tubing 13 in horizontal spacedrelation with one another.

Corresponding bars L; and M1- extend between respective lines 0, O andT, T in like manner. For convenience of construction the three pairs oflines are mounted so that the axial lines of the individual bars makeequal 60 angles with one another, although such spacing is by no meansessential to satisfactory operation of this invention. Each of theadjacent bars W and Lj are viscously coupled to one another as areadjacent bars L and M This coupling is provided by a plurality ofdevices 49, one of which is illustrated in detail in Figure '7. A pan 5%filled with a liquid 5|, such as oil, is supported above bar L by a rod52 and a plate 53 is suspended from bar M by a rod 54 so as to be freeto rotate in liquid 5| whenever bars L and W rotate relative to oneanother. Bars W and L are coupled in like manner. A drive mechanism 58is connected to the uppermost W bar to impart a reciprocating rotationthereto at right angles to the longitudinal axis of the barrepresentative of the pumping unit i0, and a stepless pawl mechanism 59is connected between the lowermost W and L bars to represent thereacting forces exerted by the downhole pump assembly 20. Mechanisms 58and 59 are described in greater detail hereinafter.

In Figure 4 there is shown a schematic representation of the torques onand displacement of the W bar interposed between lines R and R. Figure 4is a plan view of a portion of the simulator wherein bars Wi-l, Wi andWj+1 are shown as lines to facilitate explanation and wherein theserespective bars are rotated from a reference linefil) through angles 0-4, 0 and a e. {The net force F which tendsfto displace bar W1 hori-:zontally fromline 50 is equalto the difference '6 between thedisplacement force F; and the restoring force F that is:

f F 1: F1! I For small displacements so that forces F and F representthe torques acting in a. horizontaldirection on bar W1 and will be soconsidered hereinaften Equation 5 thus becomes: 7

i i+1' i+ i-1) Torque F is made up of a dynamic reaction 1 and a viscousloading term Kr(Uj+V7'), assuming bars W and L; are rotating in oppositedirections, such that Equation 6 becomes:

If the vertical distances between adjacent bars on the individual pairsof lines are equal and the rotations are small the horizontaldisplacement forces on each bar are proportional to the above-mentionedtorques. It is to be understood that the quantity I represents themoment of inertia of the bars considering the pans or plates securedthereto.

A comparison of Equations 4 and '7 reveals that they are analogous termby termexcept that the last term of Equation 4 is missing from Equation7. However, because this missing term represents the static load createdby the mass of the sucker rod it can be'neglected for purposes ofanalysis. The important quantity under consideration is the variation inexcess loading over th static value. In view of the analogy betweenEquations 4 and '7 it becomes evident that a study of various quantitiessuch as rotations, angular velocities and torques affecting thesimulator rotating lines R and R provides information regardingcorresponding quantities in the prototype sucker rod string.

Similar equations can be derived with respect to the compressive stresson the individual segments of the oil column and the motion of a generalsegment of the oil column. With reference to Figure 5, considering thenth segment 64 of the oil column as defined by the dotted lines 62 and63, let it be assumed that at a given instant the lower end of this nthsegment is displaced downward from its equilibrium position a distance gn and that the upper end or the segment is displaced downward from itsequilibrium position a distance 11111-1. This displaced position isrepresented by 64'. Such a displacement results in a compression of thenth segment by an amount ZJn-' l}n1, which in turn results in a strainso that the total compressive stress in the nth segment is In likemanner a corresponding equation can be written for the (n+1)th segmentas follows:.

The equation of motion of the oil column segment 64" which extends adistance above and below line 63 is governed by the viscous drag on theoil due to the sucker rod movement which, as previously indicated, isk1l(un|-vn) and the viscous drag on the oil due to the friction againstthe tube which is represented by koZ(un+/J.). The bottom of this lastmentioned segment is subjected to a compressive force qn+1 and the topof the segment is subjected to a compressive force qn. Finally, theweight of the oil per unit length must be considered in the equation ofmotion which, therefore, becomes:

The basic oil column equation is realized by combining Equations 8, 9,and 10 to obtain:

A comparison of Equations 11 and 13 reveals that they are analogous termby term except that the last term of Equation 11 is missing fromEquation 13. However, since this missing term represents the static loadcreated by the mass of the oil column it can also be neglected in theanalysis. In view of the analogy between Equations 11 and 13 it becomesevident that lines-O, O simulate the action of the oil column in thepump ing system.

The movement of the tubing is governed generally by the same equationsas the movement of the sucker rod. With reference to Figure 6,considering the nth segment 14 of the tubing as defined by the dottedlines 12 and 13, let it be assumed that at a given instant the lower endof this nth segment is displaced downward from its equilibrium positiona distance 211 and the upper end of the segment is displaced downwardfrom its equilibrium position a distance Z11.-1. This displaced positionis represented by 14'. Such a displacement results in a stretching ofthe nth segment by an amount Z11.-Z1L-1, which in turn results in astrain so that the total stress in the nth segment oecomes:

8. 1( n-zn-1) In like manner a corresponding equation can be written forthe (n+1) th segment as follows:

The equation of motion of the tube segment 14", which extends a distanceabove and below line '13 is governed by a total tension p"+1 on thebottom of the segment, a total tension on the top of the segment, theviscous drag aut m produced by friction of the oil column against thetubing and an upward vis cous drag k l produced by oil or other fluidpositioned between the casing and the tubing. This latter term need onlybe considered for the particular segments wherein oil is includedbetween the casing and tubing. Accordingly, the equation of motion ofthis last mentioned segment is as follows:

The basic tubing equation is realized by combining Equations 14, 15, and16 to obtain:

Equation 17 also has its counterpart in the analogue system of Figure 2.The equation of motion of the rotating bars M corresponds to Equation 6and can be written as follows:

Torque H is made up of a dynamic reaction C 6 and a viscous loading termKo(V;i+Dj) such that Equation 18 becomes:

A comparison of Equations 17 and 19 reveals that they are analogous termby term except that the last two terms of Equation 1'? are missing fromEquation 19. However, since this last missing term represents the staticload created by the mass of the tubing it can also be neglected in theanalysis as can the next to the last term because an is negligible. Inview of the analogy between Equations 1? and 19 it becomes evident thatlines T, T simulate the action of the tubing in the pumping system.

From the foregoing description, it will he evi-- dent that the simulatorillustrated in Figure 2 is an analogue of the pumping system of Figurel. The actual pumping system obviously can be divided into as manysegments as desired, each such segment being represented by acorresponding set of bars W, L, and M in the apparatus of Figure 2, theaccuracy becoming greater with an increasing number of segments.

As stated, the rotating bar system thus far described simulates thesuclzer rod string together with its associated oil column and tubing.The top of the tubing string is anchored at the surface so that it mustremain stationary, that is, its displacement must be zero at all times.This condition is represented in Figure 2 by anchoring the top bar M tobracket 19 to prevent rotation thereof. v q

The prototype sucker rod string is driven at its top end by drivemechanism l which includes points sion at point I69.

the prime mover, flywheel, crank and walking beam of Figure 1. Forpresent purposes, it is assumed that the reaction of the sucker rodsystem upon the drive mechanism is negligible, which is true in certainpractical applications and where results are desired only to apredetermined degree of accuracy, so that the motion at the top end ofthe sucker string can be expressed as a sinusoidal function. In theillustrated embodiment of this invention such driving motion is impartedto the sucker rod line by the mechanism 58 shown in Figure 9. Anelectric motor 89 is connected through a speed reducing gear train BI toa rotatable disk 82. An arm'83 is pivotally connected at one end to disk82 and at its other end to one end of a rod 84 which is constrained byguides 85 for axial movement. The other end of rod. 84 is connected tothe lowermost bar W of lines R, R to impart reciprocating rotary motionthereto. From an inspection of Figures 1 and 9 it can be seen that motor80, gear train BI, disk 82, arm 83 and rod 84 simulate, respectively,engine 29, cable 30, wheel 21, cable 28, crank 26, pitman 25 and walkingbeam 24 of the prototype pumping system.

A mechanical device known as a stepless pawl is employed to simulate theaction of the valve and pump assembly disposed in the lower region ofthe bore hole. This stepless pawl is shown diagrammatically in Figure 8as comprising a pair of rotatable pulleys 90 and which are mounted on acommon shaft 92. A third pulley 84 is connected by a yoke 96 and a wire9'! to the lowermost bar L at its end. Wire 9's passes around a guidepulley 98, and yoke 96 is freely suspended by a cable 99 attached to asupport IBil. An inextensible cable IIJI is connected at one end to thelowermost sucker rod bar W at its end. From bar W cable IIII circlespulley 9c, thence around pulley 94 back around 9| and is finally securedto an anchor post I92. A weight IE3 is fastened to bar L by means of acable I04 which passes over a fixed pulley I65.

Weight I63 serves to maintain a tension at I05 and III! in cable IOI.When the sucker rod bar rotates away from this assembly tension appearsat point I08 and slack at point its. When the sucker-bar wire movestoward the assembly slack appears at point I03 and ten- Under the firstcondition pulleys 9B and @I rotate in the direction indicated by thearrow. Under the second condition the cable slips over pulley 9B andboth pulleys 9i] and QI are held stationary because there is tension inthe cable on both sides of pulley SI at points In! and I69. This actionis analogous to that of the pump assembly at the bottom of the suckerrod string. On the upstroke oil is lifted by the pump plunger and on thedownstroke the oil is held stationary by the check valve. In thestepless pawl assembly the rotation of pulleys 90 and ill isintermittent and in one direction only. Accordingly, the total rotationof these pulleys is a measure of the total quantity of oil produced.This rotation can be determined visually by positioning a suitable scaleIIO adjacent a pointer I I I on pulley 90, or the rotation can berecorded through suitable mechanical or electrical linkage well known inthe art. The oscillatory rotation imparted to the oil column wires isthrough this stepless pawl assembly analogous to the compressional wavesset up in the oil column by the pump action in the prototype system. g

The only points in the surface pumping system that are convenientlyaccessible for making measurements are the pumping engine and thepolished rod. In this regard it has been concluded that dynamometermeasurements on the polished rod provide the best indication of thesystem's behavior. A dynamometer card illustrating such behavior can beobtained by mounting a strain gage on the polished rod to measure theforce axis. The displacement axis can be obtained by a suitablemechanical linkage system coupled to the polished rod to measuredisplacements. These two quantities are plotted together to provide aconventional dynamometer card.

Measurements corresponding to the polished rod dynamometer card areobtained in accordance with this invention. With reference to Figure 9 astress responsive element H5 is shown as being mounted between disk 8|in the driver assembly and the uppermost sucker-rod bar W. Element H5can be a carbon microphone button or a strain gage. Voltage source I I6is connected in series therewith. The tension on element II5 varies itselectrical resistance in a manner which is proportional to the forceapplied to the suckerrod wire. The resulting voltage signal is amplifiedby a suitable amplifier I I1 and applied to the vertical deflectionplates of a cathode ray oscilloscope I I9 to provide the force axis. Thedisplacement axis is obtained through a capacitive pickup. A highfrequency electrical signal, 10 kilocycles, for example, is applied tothe conductive sucker-rod wire R by an oscillator I20. Each of therotating bars W can thus be employed as one plate of a pickup condenser.This is made possible by constructing bars W of conductive material orby positioning such a conductive plate thereon in contact with wire R.In order to simulate the polished rod dynamometer card the bar W nearestthe surface unit is selected. The second plate of the pickup condenseris in the form of a metallic plate I2I mounted directly under bar W. Theopposing area presented by the bar and plate to one another thereforevaries as the bar W oscillates. Accordingly, the amplitude of theelectrical signal picked up by the capacitor plate I2I varies as thedisplacement of the driving point bar W. The output of the pickup isamplified and demodulated by a conventional circuit I23 to provide anelectrical signal, the amplitude of which is representative of thedisplacement of the uppermost sucker-rod line bar W. This demodulatedsignal is applied to the horizontal deflecting plates of oscilloscope IIt to provide the displacement axis. As previously mentioned theindividual displacements are small and thus represent the angulardisplacements and the applied forces represent torques.

The simulator of this invention thus provides a means for analyzing thebehavior of a suckerrod pumping system when the operating conditions andthe actual dynamometer measurements of the polished rod are known. Thesimulator constants and scale factors first are determined from thephototype system constants and operation conditions are calculated fromthe known rod and tube sizes, oil density and pump stroke rate of theactual pumping system. The valve and pump operation then is varied untilthe signal provided by oscilloscope H9 corresponds to the actualdynamometer card of the polished rod. Such a correspondence can beobtained by varying the speed of operation of the pump unit. When thesimulator and previously determined dynamometer measurements correspondto one another, the behavior of the vibrating loaded lines can beobserved and the motion of the rotating bars recorded through the use ofcapacitive pickups similar to that used to generate the polished roddisplacement axis. In this manner the behavior of the downhole portionof the system can be studied and the type of behavior responsible forthe various characteristic features of the dynamometer measurements canbe determined. Furthermore, optimum operating conditions for theprototype pumping system can be determined by this same means and adynamometer pattern derived which when obtained by the prototype pumpingsystem assures such optimum conditions oi operation.

While this invention'has been described in conjunction with a presentpreferred embodiment thereof, it is to be understood that thisdescription is illustrative only and is not intended to limit theinvention.

What is claimedis:

l. Apparatus for simulating. a downhole pumping system including asucker rod string, tubing surrounding said sucker rod string, and an oilcolumn between said rod and said tubing co 1-? prising three pair offlexible linesdisposedin generally parallel vertical relationship, aplurality of bars attached between said lines in each pair of lines inspaced relation, each individual bar representing, respectively, asucker rod segment, a tubing segment and an oil column segment, meansviscously coupling the individual bars rep resenting the sucker rodsegments to adjacent individual bars representing the oil columnsegments to simulate the actual viscous drag between adjacent rodsegments and oil segments, and means viscously coupling the individual,bars representing the tubing segments to adjacent individual barsrepresenting the oil column segments to simulate the actual viscous dragbetween adjacent tubing andoil column segments. 2. The, combination inaccordance with claim 1, whereineach of said coupling means, comprisesaliquid filled pan supported by one ofsaid bars and aplate suspendedfrom an adjacent bar and extending therefrom into said pan wherebyrelative. motion between adjacent bars results in movement of said platethrough the liquidin said pan to create a viscous drag between said panand said plate,

3QApparatus for simulating a segment of a downhole pumping unitincluding a rod segment, a tubing segment, and an oil column segmentcomprising, in combination, three bars, eachrepresenting one of saidsegments, meansfor suspending each of said bars for rotary movement insubstantially a horizontal direction, means.

a liquid filled pan supporecl by one of said bars,

and a plate secured to an adjacent bar and extending therefrom into saidpan whereby relative motion between adjacent bars results in move,- mentof said plate through the liquid in said pan to create. a viscous dragbetween'said pan and said plate.

5, Apparatus for simulatingadownhole pump ing system including a suckerrod string, tubing surrounding said sucker rod string, an oil columnbetween said rod and said tubing, a pumping unit driving the uppermostsucker rod, and a downhole pump driven by the lowermost sucker rodcomprising three pair of flexible lines disposed in generally parallelvertical relationship, a plural ity of bars attached between said linesin each pair of lines in spaced relation, each individual barrepresenting, respectively, a sucker rod segment, a tubing segment andan oil column segment, means viscously coupling the individual barsrepresenting the sucker rod segments to adjacent individual barsrepresenting the oil column segments to simulate the actual viscous dragbetween adjacent rod segments and oil segments, means viscously couplingthe individual bars representing the tubing segments to adjacentindividual bars representing the oil column segments to simulate theactual viscous drag between adjacent tubing and oil column segments,means to impart reciprocating rotary motion tothe bar at one end of thepair of lines representing the sucker rod string to simulate the pumpingunit driving the uppermost sucker rod, and means to measure motion ofthe bar at the second end ofthe line representing the sucker rod stringwhich simulates the action of the downhole pump driven by the lowermostsucker rod.

6. The combination in accordance with claim 5 wherein said means toimpart reciprocating motion comprises a rod attached at one end to thebar attached at said one end of the sucker rod lines, said rod beingconstrained for linear movement, a cam coupled to said rod, and a motorcoupled to said 0311113130 provide rotation thereof wherebyreciprocating motion is imparted to the bar attached at said one end ofthe sucker rod lines.

7. The combination in accordance with claim 6 furthercomprising anelectrical resistance strain responsive element secured to said rod, asource of electrical energy connected in circuit with said strainresponsive element, and circuit means to establish a voltageproportional to the stress on said strain responsive element.

8. The combinationin accordance with claim S-Wherein, said means tomeasuremotion of the bar attached at said second end of the linesrepresenting the sucker rod string comprises first and second pulleysmounted on a common rotatable shait, a third pulley having its shaftconnected to the bar attached at said second end of the linesrepresenting the oil column, a rigid support, an inextensible linesecured at one end to the line representing said sucker rod string, saidinextensibleline circling said first pulley, said third pulley, and saidsecond pulley in the order stated and being connected at its second endto said support, tension supplying means connected to said lastmentioned bar to retain said inextensible line under tension, and meansto measure rotation of said first and second pulleys which simulates thequantity of oil pumped.

9. Apparatus for simulating the action of a pump positioned in a borehole and driven by a sucker rod string v extending to the surface of thebore hole comprising two pair of vertical lines simulating respectivelythe sucker rod string and thecolumn of oil pumped to the surface withinthe well tubing, means to impart reciprocating motion to one end of saidpairof sucker rod lines to simulate the pump driving the-uppermost,sucker. rod, said two pair of .lines, being viscously coupled tosimulate the viscous coupling between the sucker rod and oil column,first and second pulleys mounted on a common rotatable shaft, a thirdpulley having its shaft connected to one of the oil column lines at theend thereof which represents the bottom of the bore hole, a rigidsupport, an inextensible line secured at one end to one of the suckerrod lines near the end thereof which represents the bottom of th borehole, said inextensible line circling said first pulley, said thirdpulley, and said second pulley in the order stated and being connectedatits second end to said rigid support, means to apply a tension to saidlast mentioned oil column line to retain said inextensible line undertension, and means to measure rotation of said first and second pulleyswhich simulates the quantity of oil pumped.

10. Apparatus for simulating a downhole pumping system including asucker rod strin tubing surrounding said sucker r'od string, an oilcolumn between said rod and said tubing, and a pumping unit driving theuppermost sucker rod comprising three pair of flexible lines disposed ingenerally parallel vertical relationship, a plurality of bars attachedbetween each line of said pairs of lines in spaced relation, eachindividual bar representing, respectively, a sucker rod se ment, atubing segment and an oil column segment, means viscously coupling theindividual bars representing the sucker rod segments to adjacentindividual bars representing the oil column segments to simulate theactual viscous drag between adjacent rod segments and oil segments,means viscously coupling the individual bars representing the tubingsegments to adjacent individual bars representing the oil columnsegments to simulate the actual viscous drag between adjacent tubing andoil column segments, means to impart transverse reciprocating rotarymotion to one end of the pair of lines representing the sucker rodstring to simulate the pumping unit driving the uppermost sucker rod,and means to measure the rotation of any selected bar which representsthe motion of th corresponding segment simulated thereby.

11. The combination in accordance with claim wherein said last mentionedmeans comprising a source of electrical energy applied to the individualbar whose motion is to be measured, said bar being constructed at leastin part of an electrically conductive material, a plate of electricallyconducting material positioned adjacent said rotating bar therebyforming a condenser with said bar, and means to measure the potentialinduced on said plate representing the distance said bar is rotated fromsaid plate.

12, Apparatus for simulating a downhole pumping system including asucker rod string, tubing surrounding said sucker rod string, an oilcolumn between said rod and said tubing, a pumping unit driving theuppermost sucker rod, and a downhole pump driven by the lowermost suckerrod comprising three pair of flexible lines disposed in generallyparallel vertical relationship, a plurality of bars attached betweeneach line of said pairs of lines in spaced relation, each individual barrepresenting, respectively, a sucker rod segment, a tubing segment andan oil column segment, means viscously coupling the individual barsrepresenting the sucker rod segments to adjacent individual barsrepresenting the oil column segments to simulate the actual viscous dragbetween adjacent rod segments and oil segments, means viscously couplingthe individual bars representing the tubing segments to adjacentindividual bars representing the oil column segments to simulate theactual viscous drag between adjacent tubing and oil column segments;means to impart reciprocating rotary motion to on end of the linerepresenting the sucker rod string to simulate the pumping unit drivingthe uppermost sucker rod comprising a rod attached at one end to one endof one of said sucker rod lines, said rod being constrained for linearmovement, a cam coupled to said rod, and a motor coupled to said cam toprovide rotation thereof whereby reciprocating rotary motion is impartedto said sucker rod lines; and means to measure motion of the second endof the lines representing the sucker rod string which simulates theaction ofthe downhole pump driven by the lowermost sucker rod comprisingfirst and second pulley mounted on a common rotatable shaft, a thirdpulley having its shaft connected to one of the lines representing theoil column, a rigid support, an inextensible line secured at one end toone of the lines representing said sucker rod string, said inextensibleline circling said first pulley, said third pulley, and said secondpulley in the order stated and being connected at its second end to saidsupport, tension supplying means connected to the above mentioned linerepresenting the oil colunm to retain said inextensible line undertension, and means to measure rotation of said first and second pulleyswhich simulates the quantity of oil pumped.

13. The combination in accordance with claim 12 wherein each of saidcoupling means comprises a liquid filled pan secured to one of said barsand a plate secured to an adjacent bar and extending therefrom into saidpan whereby relative rotation between adjacent bars results in movementof said plate through the liquid in said pan to create a viscous dragbetween said pan and said plate.

4. Apparatus in accordance with claim 12 further comprising anoscilloscope, an electrical resistance strain responsive element securedto said rod, a source of electrical energy connected in circuit withsaid strain responsive element, and circuit means to establish a voltageproportional to the stress on said strain responsive element, saidvoltage being applied to one set of deflection plates of saidoscilloscope, a second source of electrical energy applied to the barattached to the lines representing the sucker rod strin representing theuppermost sucker rod segment, said bar being constructed of anelectrically conductive material, a plate of electrically conductingmaterial positioned adjacent said last mentioned rotating bar therebyforming a condenser with said bar, and means to apply the voltageinduced on said plate to the second set of deflection plates of saidoscilloscope whereby the output of said oscilloscope simulates thcombined forces on and displacements of the uppermost of said sucker rodsegments.

RAYMOND G. PIE'IY.

No references cited.

